
Test inflationary models and primordial black holes. The
power spectrum of primordial density fluctuations, which carries
imprints from the initial inflation phase, is now well known on
intermediate to large scales, thanks to the ESA's Planck cosmic
microwave background mission, as well as large-scale surveys of
galaxies. But it is poorly known at small scales (below 2 Mpc).
Very high peaks from non-gaussian density fluctuations produced at
phase transitions (e.g., QCD) or by features in the inflation
potential collapse into primordial black holes[1]}
(PBHs), while other high peaks can produce ultra-compact
mini-halos[2]} (UCMHs). PBHs have been proposed
as an alternative to an unknown particle to explain dark
matter[3]}. They could have masses down to
\(10^{-11}\,\rm M_\odot \)  (otherwise they would have evaporated by Hawking
radiation[1]}). The discovery of PBHs and/or UCMHs
would constitute a major breakthrough, both for the existence of
these objects and for constraints on inflationary
models. Conversely, the absence of UCMHs would establish upper
bounds on the amplitude of the primordial power spectrum on small
scales[5]}.
PBHs and UCMHs, if ubiquitous, could be detected by Theia by
astrometric microlensing in the \(\sim 20\)  deep, regularly cadenced
Theia fields (\(5\,\rm deg^2\)  in total). Other astronomical objects
may mimic as PBHs or UCMHs, but stars and brown dwarfs should be
directly observable by launch date out to 1 kpc, drastically
reducing the false detections.

Stochastic background of gravitational waves. The
distortions to spacetime from gravitational waves (GWs) cause
coherent distortions in the motions of stars in our Galaxy at
locations that vary in time at the speed of
light[6]} (0.3 pc per year). The QCD transition
produces a stochastic background of GWs whose low frequencies are
inaccessible to LISA or successors of LIGO, but well matched to
Theia [7]} and Gaia [6]}. Theia will be complementary to Gaia in searching for coherent proper
motions: Gaia will have 700 times more sky coverage than Theia at
galactic latitudes \(|b| < 5^\circ \) , but the detectability of
coherent motions scales as proper motion precision over the square
root of number of stars, and the 23 times higher proper motion
precision of Theia's Deep Fields, will make it competitive with
Gaia 10-year. Both Theia and Gaia should be more competitive than
planned pulsar timing timing arrays (EPTA, etc.).

